The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to a method for measuring flow and for producing NMR images of flowing or moving subjects.
Any nucleus which possesses a magnetic moment attempts to align itself with the direction of the magnetic field in which it is located. In doing so, however, the nucleus precesses around this direction at a characteristic angular frequency (Larmor frequency) which is dependent on the strength of the magnetic field and on the properties of the specific nuclear species (the magnetogyric constant .gamma. of the nucleus). Nuclei which exhibit this phenomena are referred to herein as "spins".
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B.sub.0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. A net magnetic moment M.sub.z is produced in the direction of the polarizing field, but the randomly oriented magnetic components in the perpendicular, or transverse, plane (x-y plane) cancel one another. If, however, the substance, or tissue, is subjected to a magnetic field (excitation field B.sub.1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, M.sub.z, may be rotated, or "tipped", into the x-y plane to produce a net transverse magnetic moment M.sub.t, which is rotating, or spinning, in the x-y plane at the Larmor frequency. The degree to which the net magnetic moment M.sub.2 is tipped, and hence the magnitude of the net transverse magnetic moment M.sub.t depends primarily on the length of time and the magnitude of the applied excitation field B.sub.1.
The practical value of this phenomenon resides in the signal which is emitted by the excited spins after the excitation signal B.sub.1 is terminated. In simple systems the excited spins induce an oscillating sine wave signal in a receiving coil. The frequency of this signal is the Larmor frequency, and its initial amplitude, A.sub.0, is determined by the magnitude of the transverse magnetic moment M.sub.t. The amplitude, A, of the emission signal decays in an exponential fashion with time, t: EQU A 32 A.sub.O e.sup.-t/T*.sub.2
The decay constant 1/T*.sub.2 depends on the homogeneity of the magnetic field and on T.sub.2, which is referred to as the "spin-spin relaxation" constant, or the "transverse relaxation" constant. The T.sub.2 constant is inversely proportional to the exponential rate at which the aligned precession of the spins would dephase after removal of the excitation signal B.sub.1 in a perfectly homogeneous field.
Another important factor which contributes to the amplitude A of the NMR signal is referred to as the spinlattice relaxation process which is characterized by the time constant T.sub.1. It describes the recovery of the net magnetic moment M to its equilibrium value along the axis of magnetic polarization (z). The T.sub.1 time constant is longer than T.sub.2, much longer in most substances of medical interest.
The NMR measurements of particular relevance to the present invention are called "pulsed NMR measurements". Such NMR measurements are divided into a period of excitation and a period of signal emission. Such measurements are performed in a cyclic manner in which the NMR measurement is repeated many times to accumulate different data during each cycle or to make the same measurement at different locations in the subject. A wide variety of preparative excitation techniques are known which involve the application of one or more excitation pulses (B.sub.1) of varying magnitude, duration and direction. Such excitation pulses may have a narrow frequency spectrum (selective excitation pulse), or they may have a broad frequency spectrum (nonselective excitation pulse) which produces transverse magnetization M.sub.t over a range of resonant frequencies. The prior art is replete with excitation techniques that are designed to take advantage of particular NMR phenomena and which overcome particular problems in the NMR measurement process.
When utilizing NMR to produce images, a technique is employed to obtain NMR signals from specific locations in the subject. Typically, the region which is to be imaged (region of interest) is scanned by a sequence of NMR measurement cycles which vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques. To perform such a scan, it is, of course, necessary to elicit NMR signals from specific locations in the subject. This is accomplished by employing magnetic fields (G.sub.x, G.sub.y, and G.sub.z) which have the same direction as the polarizing field B.sub.0, but which have a gradient along the respective x, y and z axes. By controlling the strength of these gradients during each NMR cycle, the spatial distribution of spin excitation can be controlled and the location of the resulting NMR signals can be identified.
NMR data for constructing images can be collected using one of many available techniques, such as multiple angle projection reconstruction and Fourier transform (FT). Typically, such techniques comprise a pulse sequence made up of a plurality of sequentially implemented views. Each view may include one or more NMR experiments, each of which comprises at least an RF excitation pulse and a magnetic field gradient pulse to encode spatial information into the resulting NMR signal. As is well known, the NMR signal may be a free indication decay (FID) or a spin-echo signal.
The preferred embodiments of the invention will be described in detail with reference to a variant of the well known FT technique, which is frequently referred to as "spinwarp". The spin-warp technique is discussed in an article entitled "Spin Warp NMR Imaging and Applications to Human Whole-Body Imaging" by W. A. Edelstein et al., Physics in Medicine and Biology, Vol. 25, pp. 751-756 (1980).
Briefly, the spin-warp technique employs a variable amplitude phase encoding magnetic field gradient pulse prior to the acquisition of NMR signals to phase encode spatial information in the direction of this gradient. In a two-dimensional implementation (2DFT), for example, spatial information is encoded in one direction by applying a phase encoding gradient (G.sub.y) along that direction, and then a signal is acquired in the presence of a read-out magnetic field gradient (G.sub.x) in a direction orthogonal to the phase encoding direction. The read-out gradient present during the spin-echo acquisition encodes spatial information in the orthogonal direction. In a typical 2DFT pulse sequence, the magnitude of the phase encoding gradient pulse G.sub.y is incremented (.DELTA.G.sub.y) in the sequence of views that are acquired during the scan to produce a set of NMR data from which an entire image can be reconstructed.
There are a number of well known NMR techniques for measuring the motion, or flow of spins within the region of interest. These include the "time-of-flight" method in which a bolus of spins is excited as it flows past a specific upstream location and the state of the resulting transverse magnetization is examined at a downstream location to determine the velocity of the bolus. This method has been used for many years to measure flow in pipes, and in more recent years it has been used to measure blood flow in human limbs. Examples of this method are disclosed in U.S. Pat. Nos. 3,559,044; 3,191,119; 3,419,793; and 4,777,957.
A second flow measurement technique is the inflow/outflow method in which the spins in a single, localized volume or slice are excited and the change in the resulting transverse magnetization is examined a short time later to measure the effects of excited spins that have flowed out of the volume or slice, and the effects of differently excited spins that have flowed in to the volume or slice. Examples of this method are described in U.S. Pat. Nos. 4,574,239; 4,532,473; and 4,516,582.
A third technique for measuring motion or flow relies upon the fact that an NMR signal produced by spins flowing through a magnetic field gradient exhibits a phase shift which is proportional to velocity. For flow that has a roughly constant velocity during the measurement cycle the change in phase of the NMR signal is given as follows: EQU .DELTA..phi.=.gamma.M.sub.1 v (1)
where M.sub.1 is the first moment of the magnetic field gradient, .gamma. is the gyromagnetic ratio and v is the velocity of the spins. To eliminate errors in this measurement due to phase shifts caused by other sources, it is common practice to perform the measurement at least twice with different magnetic field gradient moments. The difference in phase at any location between the two measurements is then as follows: EQU .DELTA..phi.=.gamma..DELTA.M.sub.1 v (2)
By performing two complete scans with different magnetic field gradient moments and subtracting the measured phases in the reconstructed images at each location in the data arrays, a phase map is produced which accurately measures the velocity of constantly moving spins in the direction of the gradient field. Thus, where the direction of flow is known, or the flow component in only one direction is desired, two measurement cycles are required.
When it is desired to measure the velocity of spins flowing in an unknown direction, more than two NMR measurement cycles are required. For example, in the conventional six point method two phase measurements are made along each Cartesian coordinate x, y and z to measure the velocity component vx, vy and vz along each axis. The total speed is then calculated as: ##EQU1## where v.sub.x =(.phi..sub.x1 -.phi..sub.x2)/.gamma..DELTA.M.sub.x1
v.sub.y =(.DELTA..sub.y1 -.phi..sub.y2)/.gamma..DELTA.M.sub.y1 PA1 v.sub.z =(.phi..sub.z1 -.phi..sub.z2)/.gamma..DELTA.M.sub.z1 PA1 .DELTA.M.sub.x1, .DELTA.M.sub.y1, .DELTA.M.sub.z1 =change in motion encoding gradient first moment between each pair of measurements, along x, y, and z respectively, PA1 .phi..sub.x1, .phi..sub.x2, .phi..sub.y1, .phi..sub.y2, .phi..sub.z1, .phi.z2=measured phase.
When compared to the two point measurement of known flow direction, the six-point measurement takes three times as long to perform and the signal-to-noise ratio in the measured velocity is neither improved nor diminished.
Flow can also be measured in an unknown direction using a simple four point measurement. The six point method is composed of three pairs of measurements, and each pair can be thought of as a reference measurement and a flow encoding measurement along one of the Cartesian coordinates. If the same reference measurement (no flow encoding) is used with all three flow encoding measurements, then only four measurements are required. If the four measurements are .phi..sub.ref, .phi..sub.x, .phi..sub.y, .phi..sub.z, then the measured velocity components are: ##EQU2## The total speed is then calculated according to equation (3).
While the simple four point method enables the total measurement time to be reduced by 33% over the six point method, measurement errors increase. This is due to the fact that a common reference measurement is used and the errors in each component measurement v.sub.x, v.sub.y and v.sub.z are correlated. It can be shown that the variance (.sigma..sup.2) of the simple four point method is twice that of the six point method when the flow direction has equal components along each measurement axis. In some directions the variance is lower than that of the 6 point method, and, averaged over all directions, the two methods have equal variance.